List of top Questions asked in GATE Electronics and Communication Engineering

An NMOS transistor operating in the linear region has \(I_{DS} = 5 \, \mu{A}\) at \(V_{DS} = 0.1 \, {V}\). Keeping \(V_{GS}\) constant, the \(V_{DS}\) is increased to \(1.5 \, {V}\). Given that: \[ \mu_n C_{ox} \frac{W}{L} = 50 \, \mu{A}/{V}^2, \] the transconductance at the new operating point (in \(\mu{A}/{V}\), rounded off to two decimal places) is \(\_\_\_\_\).

A non-degenerate n-type semiconductor has \(5\%\) neutral dopant atoms. Its Fermi level is located at \(0.25 \, {eV}\) below the conduction band (\(E_C\)) and the donor energy level (\(E_D\)) has a degeneracy of \(2\). Assuming the thermal voltage to be \(20 \, {mV}\), the difference between \(E_C\) and \(E_D\) (in \({eV}\), rounded off to two decimal places) is \(\_\_\_\_\).

The photocurrent of a PN junction diode solar cell is \(1 \, {mA}\). The voltage corresponding to its maximum power point is \(0.3 \, {V}\). If the thermal voltage is \(30 \, {mV}\), the reverse saturation current of the diode (in \({nA}\), rounded off to two decimal places) is \(\_\_\_\_\).

In the network shown below, maximum power is to be transferred to the load \(R_L\). The value of \(R_L\) (in \(\Omega\)) is \(\_\_\_\_\). \begin{center} \includegraphics[width=8cm]{62.png} \end{center}

The radian frequency value(s) for which the discrete-time sinusoidal signal: \[ x[n] = A \cos(\Omega n + \pi/3) \] has a period of 40 is/are \(\_\_\_\_\).

The relationship between any \(N\)-length sequence \(x[n]\) and its corresponding \(N\)-point discrete Fourier transform \(X[k]\) is defined as: \[ X[k] = \mathcal{F}\{x[n]\}. \] Another sequence \(y[n]\) is formed as: \[ y[n] = \mathcal{F}\{\mathcal{F}\{\mathcal{F}\{x[n]\}\}\}. \] For the sequence \(x[n] = \{1, 2, 1, 3\}\), the value of \(y[0]\) is \(\_\_\_\_\).

Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of \(100 \, {nm}\), a fixed positive oxide charge of \(10^{-8} \, {C/cm}^2\) at the oxide-silicon interface, and a metal work function of \(4.6 \, {eV}\). Assume that the relative permittivity of the oxide is \(4\), and the absolute permittivity of free space is \(8.85 \times 10^{-14} \, {F/cm}\). If the flatband voltage is \(0 \, {V}\), the work function of the p-type silicon (in eV, rounded off to two decimal places) is \(\_\_\_\_\).

Consider the matrix: \[ \begin{bmatrix} 1 & k
2 & 1 \end{bmatrix}, \] where \(k\) is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?

A lossless transmission line with characteristic impedance \(Z_0 = 50 \, \Omega\) is terminated with an unknown load. The magnitude of the reflection coefficient is \(|\Gamma| = 0.6\). As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in \(\Omega\)) is \(\_\_\_\_\).

Let \(X(t) = A \cos(2\pi f_0 t + \theta)\) be a random process, where amplitude \(A\) and phase \(\theta\) are independent of each other, and are uniformly distributed in the intervals \([-2, 2]\) and \([0, 2\pi]\), respectively. \(X(t)\) is fed to an 8-bit uniform mid-rise type quantizer. Given that the autocorrelation of \(X(t)\) is: \[ R_X(\tau) = \frac{2}{3} \cos(2\pi f_0 \tau), \] the signal-to-quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is \(\_\_\_\_\).

For the two-port network shown below, the value of the \(Y_{21}\) parameter (in Siemens) is \(\_\_\_\_\). \begin{center} \includegraphics[width=8cm]{60.png} \end{center}

In the circuit below, the opamp is ideal. If the circuit is to show sustained oscillations, the respective values of \(R_1\) and the corresponding frequency of oscillation are \(\_\_\_\_\). \begin{center} \includegraphics[width=8cm]{50.png} \end{center}

Let \(F_1, F_2,\) and \(F_3\) be functions of \((x, y, z)\). Suppose that for every given pair of points \(A\) and \(B\) in space, the line integral: \[ \int_C \left(F_1 dx + F_2 dy + F_3 dz\right) \] evaluates to the same value along any path \(C\) that starts at \(A\) and ends at \(B\). Then which of the following is/are true?

Consider a system \(S\) represented in state space as: \[ \frac{dx}{dt} = \begin{bmatrix} 0 & -2
1 & -3 \end{bmatrix} x + \begin{bmatrix} 1
0 \end{bmatrix} r, \quad y = \begin{bmatrix} 2 & -5 \end{bmatrix} x. \] Which of the state space representations given below has/have the same transfer function as that of \(S\)?

In the circuit shown below, the transistors \(M_1\) and \(M_2\) are biased in saturation. Their small signal transconductances are \(g_{m1}\) and \(g_{m2}\), respectively. Neglect body effect, channel length modulation, and intrinsic device capacitances. \begin{center} \includegraphics[width=6cm]{51.png} \end{center} Assuming that capacitor \(C_1\) is a short circuit for AC analysis, the exact magnitude of small signal voltage gain \(\left|\frac{v_{{out}}}{v_{{in}}}\right|\) is \(\_\_\_\_\).

The opamps in the circuit shown are ideal but have saturation voltages of \(\pm 10 \, {V}\). \begin{center} \includegraphics[width=10cm]{49.png} \end{center} Assume that the initial inductor current is \(0 \, {A}\). The input voltage (\(V_i\)) is a triangular signal with peak voltages of \(\pm 2 \, {V}\) and a time period of \(8 \, \mu {s}\). Which one of the following statements is true?

Which of the following statements is/are true for a BJT with respect to its DC current gain \(\beta\)?

The information bit sequence \(\{1 \, 1 \, 1 \, 0 \, 1 \, 0 \, 1 \, 0 \, 1\}\) is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is \(C(x) = x^4 + x + 1\). The encoded sequence of bits is \(\_\_\_\_\).

A source transmits a symbol \(s\), taken from \(\{-4, 0, 4\}\) with equal probability, over an additive white Gaussian noise channel. The received noisy symbol \(r\) is given by \(r = s + w\), where the noise \(w\) is zero mean with variance 4 and is independent of \(s\). Using: \[ Q(x) = \frac{1}{\sqrt{2\pi}} \int_x^\infty e^{-\frac{t^2}{2}} dt, \] the optimum symbol error probability is \(\_\_\_\_\).

A full-scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a normalized power of 1 W, and the total noise and distortion normalized power is \(10 \, \mu {W}\). The effective number of bits (rounded off to the nearest integer) of the ADC is \(\_\_\_\_\).

Consider two continuous-time signals \(x(t)\) and \(y(t)\) as shown below. If \(X(f)\) denotes the Fourier transform of \(x(t)\), then the Fourier transform of \(y(t)\) is \(\_\_\_\_\). \begin{center} \includegraphics[width=8cm]{44.png} \end{center}

The sequence of states (\(Q_1 Q_0\)) of the given synchronous sequential circuit is \(\_\_\_\_\). \begin{center} \includegraphics[width=10cm]{42.png} \end{center}

Let \(z\) be a complex variable. If \(f(z) = \frac{\sin(\pi z){z^2 (z - 2)}\) and \(C\) is the circle in the complex plane with \(|z| = 3\), then:} \[ \oint_C f(z) \, dz \] is \(\_\_\_\_\).

A continuous-time signal \(x(t) = 2 \cos(8\pi t + \pi/3)\) is sampled at a rate of 15 Hz. The sampled signal \(x_s(t)\) when passed through an LTI system with impulse response: \[ h(t) = \frac{\sin(2\pi t)}{\pi t} \cos(38\pi t - \pi/2), \] produces an output \(x_0(t)\). The expression for \(x_0(t)\) is \(\_\_\_\_\).